Long Division, Step by Step
Long division is short division with the working written down. Nothing new is happening, there is simply too much of it to hold in your head.
Why it goes long
Short division works while you can do each step in your head. Long division writes the same steps down.
Dividing by 7 is fine mentally, because most children know their sevens. Dividing by 23 is not, because nobody knows the 23 times table, and asking "how many 23s in 147" without writing anything is asking a child to guess. Long division exists to make that guess into a calculation, and the working underneath is not extra bureaucracy, it is the part that replaces the memory.
The four-step cycle
Divide, multiply, subtract, bring down
Divide: how many times does it go in? Write that digit on top.
Multiply: that digit times the divisor. Write it underneath.
Subtract: take it away. What is left is the remainder so far.
Bring down: pull the next digit down beside it, and start again.
Then repeat until there are no digits left to bring down. Every long division question, however large, is that cycle running two or three or five times.
One cycle, on the page
Here is 966 divided by 23 with only the first cycle done. Read it slowly, because where each number sits is the whole method.
Divide. Twenty three does not fit into 9, so take two digits: 96. Twenty three goes into 96 four times, and the 4 is written above the 6, not above the 9, because 96 is the chunk it came from. Getting that column right is what stops the final answer being ten times too big.
Multiply. 4 x 23 = 92, written directly under the 96, ones under ones.
Subtract. 96 - 92 = 4, written under the line. Four is smaller than twenty three, which is the built-in check that the 4 on top was the right size.
Bring down. The next digit of 966 is the last 6, and it comes down to sit beside the 4, making 46. That is the blue digit on the drawing, and it is the step children forget most often. Nothing has been calculated here. A digit has simply moved.
Now the cycle starts again on 46, and this time it is the last one.
Write the multiples first
Before starting, write out the first nine multiples of the divisor down the side of the page. For 23 that is 23, 46, 69, 92, 115, 138, 161, 184, 207.
It takes about thirty seconds and it converts the hardest part of the method into reading a list. Most children who find long division impossible are not failing at division at all; they are failing at guessing how many 23s fit into 147, over and over, under time pressure. Give them the list and the difficulty largely disappears.
Build the list by doubling
23, then double for 46, then 69 is 46 plus 23, then double 46 for 92. You rarely need all nine, and you almost never need to work each one out from scratch.
A full example
Now the same method on a sum that does not come out exactly. Follow the drawing as you read.
Work out 500 divided by 16.
- List: 16, 32, 48, 64, 80, 96, 112, 128, 144.
- Sixteens do not fit into 5, so take two digits: 50. From the list, 48 fits and 64 does not, so the digit is 3 and it goes above the first 0, because 50 is the chunk it divided. Subtract: 50 - 48 = 2.
- Bring the last 0 down beside the 2 to make 20. Sixteen fits once, so write 1 and subtract: 20 - 16 = 4.
- There is nothing left to bring down, so the 4 stays as a remainder.
31 remainder 4
Check it by multiplying back
31 x 16 = 496, and 496 + 4 = 500. Answer times divisor, plus remainder, gets you back to where you started. It takes fifteen seconds and it catches almost every error.
Common mistakes
1. Writing the answer digit in the wrong column
Getting all the arithmetic right and putting the digits in the wrong places, so 42 comes out as 402. Look again at the drawing above: the 4 stands over the 6 of 96, because 96 was the chunk it divided. Each answer digit goes directly above the last digit of its own chunk. Squared paper is not a childish crutch here, it is the thing that makes the columns hold.
2. Leaving a subtraction result bigger than the divisor
Subtracting and getting 27 when dividing by 23. If what is left is still bigger than the divisor, another one fits, so the digit above was too small. This is the built-in check, and it catches almost every guessing error before it spreads.
3. Forgetting a zero in the middle of the answer
When the chunk is too small to divide, the answer digit is zero and you still bring the next one down. Skipping it silently makes the answer ten times too small, and it is the mistake most likely to survive a check, because everything else looks tidy.
Practice questions
Seven questions. One attempt each, and the explanation appears once the answer is in.
Check yourself
No sign up. Nothing is sent anywhere, the score stays on this device.
What to learn next
Division is what factors are made of, and a number's factors are exactly the numbers that divide it with nothing left over.
For parents
If long division is causing tears, the problem is almost never the method. Ask your child to write the nine multiples of the divisor before they start. If that alone unlocks the question, then the difficulty was guessing rather than dividing, and it is worth telling them that, because a child who believes they are bad at division will stop trying.
Still stuck on this?
Send us the question and a teacher will answer it. No charge, and you do not have to be a student here.
What to learn next
Everything in the Learning Hub
Every topic is free and every one ends with practice questions. Start anywhere.
Fractions
Math · 9 topics
What Is a Fraction?Equivalent FractionsSimplifying FractionsComparing FractionsAdding and Subtracting Fractions With the Same DenominatorAdding Fractions With Different DenominatorsFinding a Fraction of a NumberMixed Numbers and Improper FractionsFractions to DecimalsDecimals and percentages
Math · 7 topics
What Are Decimals?Comparing and Ordering DecimalsAdding and Subtracting DecimalsRounding DecimalsWhat Are Percentages?Finding a Percentage of a NumberFractions, Decimals and PercentagesScience: matter and the water cycle
Science · 5 topics
What Is Matter?Solids, Liquids and GasesChanging StateThe Water CycleMixtures and SolutionsWhole numbers
Math · 10 topics
Place Value to 1,000,000Rounding Whole NumbersAdding and Subtracting With RegroupingTimes Tables That Actually StickMultiplying by 10, 100 and 1000Long Multiplication, Step by StepShort DivisionLong Division, Step by StepFactors, Multiples and PrimesOrder of OperationsForces and energy
Science · 6 topics
Forces and MotionFrictionGravity, Mass and WeightLevers and Simple MachinesEnergy and Its FormsSimple CircuitsStuck on this topic? Get one class, free.
A tutor works through it live with your child, one on one, and sends you a short written report afterwards. No card needed.